Wednesday, December 25, 2013

Talk@UGent: Model-theoretic constructions without actual infinity (M. Czarnecki)

At 5 p.m. on January 7, Marek Czarnecki (Warsaw University) will give a talk at the Centre for Logic and Philosophy of Science (room 2.30). If you're around, feel free to drop by.

We base on the notion of FM-representability introduced by M. Mostowski as an explication of representability without actual infinity.  By Mostowski’s FM-representability theorem and Shoenfield’s Limit Lemma FM-representable notions  are  exactly  those  which  uniformly  computable  limits  of  computable notions  i.e.   which  are  constructible  in  finitistic  sense  (by  true  constructions, not constructions relative to some uncomputable oracle).
We introduce the notion of concrete models - FM-representable models - and consider the feasibility of classical model-theoretic constructions in concrete models framework.  The aim is to identify the finitistic content of model theory - the part that has a computational meaning.
More philosophically - studying concrete models provides with a better understanding of mathematical structures that are cognitively accessible and can be algorithmically learned.  They can also be used for representing epistemologically feasible approximated representations of reality and cognitively accessible semantics.

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